(a) Use Definition 2 to find an expression for the area under the curve $ y = x^3 $ from 0 to 1 as a limit.

(b) The following formula for the sum of the cubes of the first $ n $ integers is proved in Appendix E. Use it to evaluate the limit in part (a).

$$ 1^3 + 2^3 + 3^3 + \cdots + n^3 = \biggl[ \frac{n(n + 1)}{2} \biggr]^2 $$

## Discussion

## Video Transcript

Okay. The first thing we know is that Delta Axe is three minus one over ad, which is two over. And we know acts of eyes one plus items to over. And therefore, what we know is that we have the limit as UN approaches infinity starting at one like this.

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